Inverse Variation: Garrison of 120 Men has a provision for 30 days. A Garrison of 120 men has a provision of 30 days. At then end of 5 days,5 more men joined them. How many days can they sustain on remaining provision.

More or less, as TonyK indicated in a comment:

If you have enough provisions for 120 men for 30 days, then you have how many man-days of provisions? That is, how many days would the given provisions last with 1 man or how many men could the given provisions support for just 1 day?

> $120\text{ men}\cdot30\text{ days}=3600\text{ man}\cdot\text{days}$

Now, how many man-days of provisions are consumed after 5 days with 120 men? How many man-days of provisions are left?

> $120\text{ men}\cdot5\text{ days}=600\text{ man}\cdot\text{days}$ of provisions used; $3600\text{ man}\cdot\text{days}-600\text{ man}\cdot\text{days}=3000\text{ man}\cdot\text{days}$ of provisions left

Finally, with 5 more men, there are $120+5=125$ men, so how many days will the remaining provisions last?

> $$\frac{3000\text{ man}\cdot\text{days}}{125\text{ men}}=\frac{3000}{125}\text{ days}=\cdots$$